Continued from previous post under the same caption……..
Lunar(Day,month year)—(As we are discussing Lunar thing we will use the term Rashi of Indian system, not sign. Sign is a tropical concept. The figures quoted are in accordance with modern astronomy)
We have to look at the things from the perspective of both Moon and Sun travelling along ecliptic(moon’s path is inclined by 5.25 degrees with ecliptic though it also precesses around normal to ecliptic in 18.5 years) and passing through 12 Rashi in Zodiac belt in counterclockwise direction The day when Sun and Moon are at exactly same degree in ecliptic the day is called Amavasya in Indian system. Next day is the New Moon day of lighted fortnight (waxing phase). When Sun and Moon are 180 degree apart in zodiac it is Full Moon day( called Purnima in Indian system) followed by first day of dark fortnight(waning phase). One rotation of moon around earth is called one lunar day or Tithi. The numbering of Tithis in each fortnight is 1 to 15. This is also called as time taken by moon to traverse 12 degree each in ecliptic starting from its conjunction with Sun. As both Sun and Moon moves but with different velocity so while Moon comes back to the point it has started from, Sun goes ahead by around 1 Rashi. (Moon moves ahead with 27 hours as an average through one constellation or 2.5 days through one Rashi. We have mentioned that each constellation is divided into 4 quarters and each Rashi consists of such 9 such quarters.) So moon has to travel extra to catch Sun (meaning thereby it is not like making one rotation of 360 degree exactly in fixed zodiac of Rashi ). As an average 12 degree separation of Sun and Moon marks end of 1 one Lunar day(though speed of Sun,i.e. earth and Moon varies along the path yet as an average it is 13 degree of Moon’s movement minus 1 degree of Sun’s movement in the same time). Thirty(30) Tithis go to constitute one Lunar Month. The name and order of Lunar months are same as followed in Sidereal year system. But the two are completely different issue. In Sidereal system the name of the month is in accordance with constellation occupied by Full moon in the month. For example if full moon is falling in constellation Chitra(Spica 16) then the month is known as Chaitra. ( It may also be named in accordance with Sun occupying a Rashi at the time of Full moon. It is not widely used but for a few states of India like Orrisa). Lunar month may begin on either first day of lighted fortnight or first day of dark fortnight, depending upon convention of a Calendar system. In Indian Calendar system Vikarmi Samvat which keeps record as per Lunar year and Lunar month, all month begins with dark fortnight. But of course year begins with lighted fortnight of Chaitra. So, half of the Lunar month Chaitra falls in previous Lunar Year. But the solar day for a given Lunar month and Lunar day varies from year to year because of the difference in the Lunar year and Solar year and also because of the varying speed of moon that is varying length of Lunar day.
Sidereal year, as followed in other Indian Calendar system Customary Shaka, begins with first Vaishaka( the constellation occupied by full moon is Vishakha(Alpha Libra) while Sun is in Aries Rashi at around 25 degree). Sun enters in Mesha(Aries)on around 14th April which marks the beginning of sidereal year as Vaishaka 1. This beginning of sidereal Zodiac, that is Aries 0 degree, is around 180 degree opposite to the beginning of Chitra. Onward the time taken by Sun to cross different Rashi successively is called the span of month, the name of which depends upon the constellation occupied by full moon of the month. As speed of Sun varies so the length of months varies from 29 to 31 days. The beginning of sidereal Vaishaka generally falls in dark fortnight( Sidereal month does not depend upon Lunar month/day counting so beginning of month does not depend upon exact New moon or Full moon position ). Sidereal Chaitra( last month of Sidereal year) beginning always falls on around 14th march. So in Shaka all month begins in between dark fortnight and successive months and days are of fixed length falling on a fixed solar date (except for the consideration of leap year) The year begins on 13/14 April. But in Vikarmi Samvat all months and day are Lunar and begins with dark fortnight of the month which precedes lighted fortnight of the same month.
The time taken for complete rotation of moon around the Sun( which constitute one Lunar month or Tithi) varies from one month to other, but as an average it is 29.531 solar days. We know that the span of solar month ( as used in present day Gregorian Calendar) is 30.437 days as an average. The span of one Tithi varies from day to day because of variation in speed of moon. So it is not fixed when a Tithi will start in a solar day. However the pattern is repeated after every 1 lunar year which consists of 354 solar days, 8 hours and 48.5 minutes (354.36 solar days). This is the time required for 360 rotations of moon around earth which is equal to 360 lunar days or Tithis. The duration of one Tithi is 0.984533 solar days as an average. To adjust the difference one Tithi has to be omitted after 61 solar days.
As discussed, Tithis may vary in length so those don’t keep pace with solar days. Meaning thereby two solar days may cover one Tithis or two Tithi may cover one solar day. Tithis are numbered according to the Tithis falling at sunrise. So there is great deal of variation in the beginning of Lunar year in relation to solar month/days. Lunar year should not be confused with Sidereal year though month naming and order of the months is same in both. Sidereal year begins on Vaishaka 1 falling on 13/14 April with Sun entry into Aries sign, and follows a fixed cycle of various fixed number of days for the successive sidereal months( like the one followed in Gregorian Calendar). The total span of sidereal year is as discussed 365.256 days( 365 days and 6 hours and 9.16 minutes). But Lunar year begins after cycle of 354.36 solar days(354 days 8 hours and 48.55 minutes) and Lunar months are of fixed 30 Tithis in each Lunar month of Lunar year. So the beginning of Lunar year in relation to solar year varies from year to year. The cycle of new moon and full moon depends upon Titihi counting. As we will see that for Lunar year it may be some Tithi( 1 to 15) of Chaitra dark fortnight but for sidereal purpose it may be some day of Falgun( 1month back). The issue will be clearer while we will discuss Indian Luni Solar calendars–Shaka and Vikarmi Samvat.
However, only Islamic Calendar follows purely lunar system. As per Islamic Calendar Lunar year consists of 354.355 days in an average adjusted each year as per visual observation. But there is no adjustment between Lunar year and Solar Year, that is to say there is no concept of intercalary month.. .
Luni Solar:
Lunar year adjusted with sidereal or tropical year is called Luni Solar Year. This adjustment is done in only Indian Luni-solar system called Vikarmi samvat. However both system Shaka and Vikarmi Samvat are known as Luni-solar as discussed in last paragraph. Once again to remind sidereal naming of month and serial number are same as followed in pure Lunar system. But still two are completely different issue.
Due to this difference in solar month (30.437 days) and lunar month (29.531 solar days=30 Tithis) (or what we call difference in Lunar year and Solar year by around 11/12 days)1 extra lunar month is accumulated after every 32/33 solar months. Meaning thereby lunar year starts to lag behind solar year by 1 complete lunar month at the end of 32/33 solar months. So there is one extra lunar month in that year. This extra month is called intercalary month. This extra lunar solar month has to be omitted out of calendar so that again beginning of solar and lunar calendar coincide as per the convention of beginning point. All Lunar month begins on next day to Full moon(That is dark fortnight precedes lighted fortnight). However in actual Calendar system Lunar year may not necessarily start on the first day of Lunar month Chaitra. In Indian Calendar system called Vikarmi Samvat a lunar year begins on first day of lighted fortnight of Chaitra. Beginning of Lunar Chaitra, that is beginning of dark fortnight, may vary anywhere between 13/14th Feb to 13/14th March, which is sidereal month Fagun ( 1 month behind) . So beginning of Lunar year may fall anywhere between 1st march to 29th March. Generally Sun entry into Aries on 13-14 April marks the end of sidereal Chaitra and beginning of sidereal Vaishaka. So Chaitra is the last month of sidereal year. To illustrate the point if the beginning of a lunar year of Vikarmi Samvat started on 14 Chaitra of sidereal year or 27TH march then the Lunar year may end on 2nd Chaitra of sidereal year or 15th march of next year.
The rules for intercalary month are two-fold. When there are two New moons in a solar month, which happens after 32/33month, then naturally two lunar months begin in the same solar month. So the first one is called intercalary month and next one is called Pure month. The First one is omitted. Further there may happen a year when no New moon falls in a solar month, again after 32/33months. In that case the month falls short by itself. It is called decayed (Kshaya) lunar month. In such case there happens two intercalary month-one before the decayed month and one after the decayed month. In that case which one is to be considered depends upon convention.
Indian calendar system use Luni-solar concept. Shaka is Luni-sidereal. It is Luni-Solar in the sense that months are named in accordance with constellation occupied by full moon in that month. Otherwise the year is Sidereal and is of fixed length. There is no issue of adjustment between Lunar year and Solar year. Vikarmi Samvat is also Luni-solar but it follows its own system of year consisting of 360 Lunar days or 30 lunar days per month or of around solar 354.35 days. So issue of intercalary month is involved. And after 32/33months adjustment has to be done. However naming and serial number of month follows the same rule as it is followed in Shaka. So a month say Chaitra is completely different issue in Shaka and Vikarmi Samvat. For the urose of official Calendar a system of Luni-tropical year called called official Shaka is used. This starts on 22/23 march(vernal equinox day) as Chaitra 1 is used . Rest it follows the same cycle as sidereal Shaka but the length of year is tropical 365.242 days(365 days 5 hours and 48.5 minutes). For religious/astrological purpose it is either Luni-sidereal year called Customary Shaka or Vikarmi Samvat is used. So, as per Indian system, overall there are three kinds of Chaitra-Sidereal, Lunar and Official. Indian alamanc( called Panchang) keeps count on the basis of Lunar day(Tithi) of Vikarmi Samvat but it also shows, side by side,the corresponding date for Customary Shaka, Official Shaka and Gregorian Calendar. It also shows the moon’s entry into different constellations and its timing, and also Sunset/Sunrise Time. The first column shows the span of day in term of Ghati/Pal.
To be continued………
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